Multiplier



R. F. CASEY MULTIPLIER Feb. 8, 1966 IN1/Ewan. ROBERT E CASEY ATTORNEYS United States Patent O 3,234,375 MULTIPLIER Robert F. Casey, East Acton, Mass., assignor to arthur D. Little, Inc., Cambridge, Mass., a corporation of Massachusetts Filed Feb. 23, 1961, Ser. No. 91,048 1S Claims. (Cl. 23S-194) The present invention relates in general to multipliers and in particular to a novel four-quadrant analog multiplier providing a relatively wide frequency response with a relatively small number of standard components.

As is well known, a four-quadrant analog multiplier is designed to produce an output signal whose magnitude is proportional to the product of the instantaneous magnitudes of two input signals. In a four-quadrant analog multiplier, the output has a positive polarity when both input signals are of a like polarity but has a negative polarity when the input signals are of opposite polarity. While a great many types of multipliers have been previously designed, they generally have been limited by the complexity of their design, making adjustments and replacements diiicult and time consuming. They also have been limited by the cost of manufacture, often due to the use of specialized components. Moreover, they generally have not been designed to multiply signals which can vary in magnitude from a straight D.C. voltage to a highfrequency alternating voltage.

Accordingly, the object of the present invention is to provide a multiplier of novel and simple design which provides accurate products for input signal frequencies extending over a broad spectrum, including zero frequency.

A further object of the present invention is to achieve multiplication of two signals by a multiplier which comprises standard commercially available components.

A more specific object of the present invention is to provide a novel and simple multiplier which comprises a beam switching tube of the type designed to emit a sheet beam, means cooperating with the beam switching tube for switching the beam and for varying the intensity of the beam in accordance with the magnitude of two input signals which are lto be multiplied, and means cooperating with the aforesaid beam for producing an output signal whose magnitude is proportional to the product of the instantaneous magnitudes of the two input signals, the output signal having a polarity which is positive when the two input signals are of like polarity and which is negative when the two input signals are of unlike polarity, whereby to provide a true four-quadrant analog multiplier.

Other objects and many of the attendant advantages of the present invention are apparent from the following detailed specification which is to be considered together with the accompanying drawing which is a diagram of a circuit embodying the invention.

Referring now to the drawing, the illustrated circuit comprises seven vacuum tubes T1-T7. Tubes T1-T5 make up the multiplier section of the circuit, and tubes T6 and T7 make up the output section of the circuit.

Tube T1 is a beam switching tube of the type which is designed to emit a sheet beam. This type of tube is available from different manufacturers under different designations, as, for example, RCA 7360. Tube T1 cornprises two anodes 2 and 4, a cathode 6, a control grid 8, an accelerating electrode 10, and two deiiecting plates 12 and 13. The two anodes 2 and 4 are connected to a. suitable positive voltage source V+ through two plate resistors 14 and 15 respectively. The control grid 8 is connected to a voltage divider network comprising resistors 16 and 17 connected between a negative voltage 3,234,375 Patented Feb. 8, 1966 source V- and ground. The accelerating electrode 10 is coupled to the two plates 2 and 4 by way of two resistors 20 and 22 of equal magnitude. The cathode 6 is connected to the anode 24 of a pentode tube T2. The deecting plate 12 is connected to ground through two series resistors 26 and 28. The dellecting plate 13 is connected by a resistor 30 (identical in value to resistor 26), the secondary coil 32 of a transformer 34, and a resistor 36 to the slider 38 of a potentiometer which comprises a resistance element 40. The latter is an integral part of a voltage divider network consisting of resistors 44, 46, 48, and 58 which is connected between a positive voltage source V+ and the negative voltage source V-. The primary coil 52 of the transformer is connected to a high frequency oscillator 56.

The cathode 6i) of tube T2 is connected to a negative voltage source V- through a cathode resistor 62. Its control grid 64 is connected to a voltage divider network comprising resistors 66 and 68 connected between the negative voltage source B- and ground. The screen grid 70 is connected to ground. The suppressor grid 72 is tied to the cathode 26.

The deilecting plate 12 of tube T1 is connected through resistor 26 and a second resistor 76 to an input terminal 78. One of the variable signals, in this case the signal designated as X, is injected at lterminal 78. Terminal 78 is connected to ground by a resistor 8i) and is also connected to one of the control grids 82 of tube T3.

Tube T3 is a duplex triode, comprising on `one side an anode 34, the aforesaid grid 82, and a cathode 86, and on the other side a second anode 90, a control grid 92, and a cathode 94. Control grid 92 is connected directly to ground. The anode 84 is coupled to the anode 4 of tube T1; in a similar fashion, the anode 90 is coupled to the anode 2 of tube T1. The two cathodes 86 and 94 are connected through identical resistors and 162 to the anode 104 of tube T4. Connected between the two cathodes is a iixed resistor 106 and a variable resistor 10S. The tube T4 is a pentode, comprising in addition to anode 104 a cathode 112, a control grid 114, a screen grid 116, and a suppressor grid 118. The suppressor grid 118 is tied to the cathode 112, the latter in turn being connected through ya resistor 120 to the negative voltage source V+. The control grid 114 is connected to a voltage divider network comprising resistors 124 and 126 connected between the negative voltage source V- and ground. The screen grid 116 is connected directly to ground.

The tube T5 is a double triode. One section comprises an anode 138, a control grid 132, and a cathode 134. The other section comprises an anode 138, a control grid 140, and a cathode 142. The anode 1.30 is coupled by a resistor 146 to anode 4 of tube T1. The anode 138 is coupled by a yresistor 148 to anode 2 of tube T1. Resistors 146 and 148 are of equal values. The cathodes 134 and 142 are connected through identical resistors 152 and 154 to the opposite ends of a resistance element 156 which forms part of a potentiometer having a slider 158 which is connected between cathode 6 of tube T1 and anode 24 of tube T2. The two control grids 132 and 140 are connected to an input terminal 162 to which is applied the second variable signal to lbe multiplied, represented in this case as the Y input. These control grids are connected also to a Voltage divider network comprising three fixed resistors 166, 168, and connected in the order named between secondary coil 32 and ground, plus a fourth Variable resistor 172 connected between ground and the junction of resistors 166 and 168.

The tube T6 is a tetrode. Its plate 176 is connected by a plate resistor 178 to voltage source V+. Its screen grid 180 is also coupled to voltage source V+. Its control grid 182 is connected to the junction of a pair of resistors 134 and 186 which are between voltage sources V-land V- in series with load resistor 15. Its cathode 18S is lconnected to ground through a resistor 19d.

Tube T7 is a triode. Its anode 194 is connected through a plate resistor 1&6 to the voltage source V Its grid 19S is connected to the junction of a pair of resistors 200 and 202 connected between voltage sources V+ and V- in series with resistor 178. The cathode 294 of tube T7 is connected by means of a resistor 206 te the voltage source v The output is taken at the cathode of tube T7.

In the absence of any X or Y signals at terminals 73 and 162, all of the tubes will be conducting and at a steady state. The tubes T2 and T4 function as constant current generators. For the purposes of this invention, it is necessary that the two sections of tube T 3 conduct equally in the absence of an X signal. It is also neces; sary for the two sections of tube T5 to conduct equally. In this connection, it is to be observed that the grids 82 and 92 of tube T3 are at the same potential in the absence of an X signal. Accordingly, if the two sections of tube T3 were identical in all respects, the anode 84 would carry precisely the same current as the anode 90. However, since it is impossible to have two tube sections which are identical in all respects, some means must be provided for balancing the two tube sections. In this case, the two tubes are constrained to operate substantially identically by the resistors 1th) and 102. Resistor 103 performs a gain adjusting function. Since the two sections of tube T5 also may not conduct equally, provision must be made for a Y balance. This is yafforded by slider 158, the latter being positioned so that equal currents will be produced in both sections of tube T5.

The two deflecting plates 12 and 13 are at positive potentials with respect to the cathode 6. For the purposes of this invention, it is essential that in the absence of an X signal, the beam emitted by the cathode 6 will be shared equally by the anodes 2 and 4. Although in theory this should result from setting the deflecting plates 12 and 13 at equal potentials, in practice it has been found necessary to make on delecting plate more positive than the other in order to achieve equal division of current be; tween the two anodes 2 and 4. Thus, in the illustrated circuit the deflecting plate 12 is at ground potential where as the detlecting. plate 13 may be at a slightly different potential, the latter being determined by the position of slider 3S. In this connection, it is to be observed that in practice the resistor 411 will be equal to resistor 46 and the resistor 48 will be equal to the resistor Sil. Then, if the voltages of sources V- and V+ are of equal magnitude, setting the slider 3S at exactly the center of resistance 4t) will produce a zero voltage on deecting plate 13. Shifting the slider 38 to the right will render deflecting plate 13 positive, whereas shifting it to the left will render the detlecting plate more negative.

The total amount of current which is carried by each of the anodes 2 and 4 is determined in part by Athe voltages applied to the deflecting plates 12 and 13 and in part to the intensity of the beam which is emitted by the cathode 6. Since -tube T2 functions as a constant current generator, and since the relative voltages between the cathode 6 and the control grid 8 are ixed, the intensity of the beam emitted by the cathode 6 is determined by the amount of current which is bypassed through the tube T5.

The tube T1 forms the nucleus of the present invention. The fundamental concept of the present invention relies upon the beam switching characteristic of the tube T1 as well as upon the functions of the tubes T3 and T5. In general, multiplication is effected by varying the amount of current received by the vanodes 2 and 4 in accordance with the amplitudes of the X and Y signals which are applied to the input terminals 78 and 162 respectively. Variation of the X signal causes deflection of the sheet beam emitted by cathode 6, with the direction of deflection being determined by the polarity of the signal change and the amount of deflection being deter-` mined by the magnitude of the signal change. Variation of the Y signals causes a change in the amount of current from tube T2 which is bypassedby tube T5, as a result of which the intensity of the beam emitted by cathode 6 will 'also change, the direction and magnitude of the change in beam density being determined by the polarity and magnitude of the signal change.

When a positive signal voltage is applied to terminal 78, the sheet beam 6 will be deflected toward the anode 2 and away from the anode 4. The amount by which the sheet beam is deflected is determined by the magnitude of the applied X signal. The greater the positive voltage applied to the deilecting plate 12, the greater the amount of the beam which will be seen by the anode 2. In the practice of this invention, it is contemplated that themaximum voltage applied to the de ecting plate .12 will be less than the magnitude required to fully swing the sheet beam away from the anode 4 and onto the anode 2, whereby a minimum current will flow in the anode 4. When a negative X signal voltage is applied to terminal '78, the reverse phenomenon occurs. It is contemplated that the maximum negative X signal voltage will be less than the magnitude required to fully swing the beam away from anode 2, wherebyV a minimum current will ow through the anode 2. This limitation on the magnitude of the X signal is necessary since the beam is not of uniform intensity throughout its width. Without this limitation, distortion would result.

When a positive Y signal voltage is applied to terminal 162, tube T5 will conduct to a greater extentthan it does when the Y signal is zero. As a consequence, more of the current emitted from the tube T2 will flow through the tube T5 and less of the current from tube T2 will flow through cathode 6. Conversely, when the Y signal swings in a negative direction, less of the current from tube T24 will be bypassed through the tube T5, thereby causing an increase in the current through the cathode 6,. In practice, the maximum positive signal voltage applied to terminall 16,2 will never be great enough to bypass all of the current from tube T2 around tube T1, while the maximum negative signal voltage applied to terminal 162 will never be great enough to cut off tube T5. The reason for this is because otherwise the result becomes non-linear.

In order for the illustrated circuit to function as an analog multiplier, it is necessary that the output should` be Zero when one or the other of the signals X and Y is Zero since the productv of X and 0 and the product of Y and 0 always equals zero. At the same time, inporder for the illustrated invention to function as a four-quadrant multiplier, it is necessary that the output be truly indicative of the magnitude as well as the polarity of the product of X and Y when X and Y are values other than Zero. To meet these requirements, it isnecessary to establish the following parameters:

(l) At X=0, the currents passing through anodes 2 and 4 of tube T1 equal each other;

(2) At X :0 and Y=0, the current through anode 84 equals the current through anode (3) At X :0 and Y=O, the current through anode 130 equals the current through anode 138;

(4) At X=0 and Y=0, the current through load resistor 14 equals the current through load resistor 15; and

(5) Equal changes in X and Y produce incremental changes of equal magnitudes in the currents through anodes S4, 9G, 130, and 138, but the incremental change in the current through anode 2 or 4 is proportional to the change in Y for a given change in X-hence multiplication. Thus, for example, if a change in the Y signal produces av given arithmetic incremental change in the currents through anodes 13@ and 138, a change of equal magnitude in the X signal will produce an arithmetic incremental change of the same magnitude in the currents 5. through anodes 84 and 99. A given change in X produces an incremental shift in current between anodes 2 and 4 that is proportional to Y. Conversely, an incremental change in Y will produce an incremental shift in the currents of anodes 2 and 4 that is proportional ot a change in X. Hence, symmetrical multiplication.v

With these parameters established, the illustrated circuit meets the requirements of an analog multiplier, as is apparent from the description hereafter of its operation under ditferent input conditions.

1. No X signal, but a positive Y signal Assume now that there is no X signal at terminal 78 but that a positive Y signal is applied to terminal 162, tube T5 will conduct to a greater extent than normal. The increased conduction of tube T 5 effectively bypasses more of the current from tube T2, thereby decreasing the density of the current flowing from the cathode 6 to the anodes 2 and 4 in tube T1. However, since the current in the two sections of tube T5 are fed back through resistors 146 and 14S to the plate circuits of tube T1, the total amount of current carried by the plate resistors 14 and 15 will be unchanged despite the decrease in density of the ybeam current in tube T1. Therefore, the output, i.e.,V the signalapplied to Vthe control grid 182 of tube T6, will be zero. In other words, although the density of the beam in tube T1 has been changed in response to the Y signal, there will be no output signal, as is proper due to the fact that the positive Y signal was multiplied by a zeroX signal. The result is obtained if the Y signal is negative.

2. No Y signal, butin positive X signal Assume now that there is no Y signal but that a positive X signal is applied at terminal 78. The positive X signal is coupled not only to the deflecting plate 12 but also to the control grid 82 of tube T3. The positive signal applied to deecting plate 12 will cause the sheet beam emited from cathode 6 to be delected toward the anode 2 and away from the anode 4, the amount of deilection being proportional to the magnitude of the. X signal. lAt the same time, the signal applied to the control grid 82 will cause the left-hand section of tube T3 to conduct'niore than normal. The increased current through the lefthand section of tube T3 will be accompanied by a corresponding decrease in the-current of the right-hand section of the same tube, the latter decrease being due to the fact that control grid 92 is grounded and cathode 94 is tied `to cathode 85. Thus, although an increase in the current through the left-hand section of tube T3 will cause a rise in the voltage across the cathode resistor 100, ,it will also cause the cathode 94 to got more positive. Since grid 56.is tied to ground, a rise in the voltage at cathode 94 will result in a decreased current in the righthand section of tube T3. vDeflection of the sheet beam `toward the left anode 2 in response to the positive X signal results in the left anode V2 carrying more current than is carried by the right anode 4. However, since the anode 84 is connected in parallel with the anode 4 while the anode 96 is connected in parallel to the anode 2, the increased current through the left anode 2 is offset by the decreased current through anode 90 cause by the same X signal. In the same way, the reduced current through the anode 4 -serves to offset the increased current through the anode 84. Because of the established operating parameters, the total amount of current owing through the plate resistors 14 and 15 will remain unchanged for various values of X so long as the signal Y remains zero. As a consequence, `there will be nooutput signal, as is proper due to the fact that the positive X signal was multiplied by a zero VY signal. The same result is obtained if the X signal is negative.

3. Positive X and Y signals When signals are applied at both X and Y terminals, the circuit will effectively multiply them to produce an output representative of the multiplication of X and Y. The output will have a polarity indicative of the relationship between the polarities of the X and Y input signals. If one signal is positive and the other is negative, the output will also be negative. On the other hand, if the two inputs are both positive or both negative, the output will be positive. At this point, it is to be observed that the polarity of the signal applied to the control grid of tube T6 will be exactly opposite to the polarity which the multiplied output should have. However, because of the phase reversal affected by amplifier tube T6, the output signal taken at the cathode of tube T7 will have the correct polarity.

Assume now that positive X and Y signals of the game magnitude are applied to terminals 78 and 162 respectively. The X signal will cause anode S4 to carry more current and anode to carry less current. At the same time, it will cause more of the beam from cathode 6 to pass through anode 2 and less through anode 4, the deflection being sucient for the decreased current through anode 4 to balance the increased current through anode 84 in the absence of any change in intensity of the beam. However, since simultaneously the Y signal will cause a decrease in intensity of the beam from cathode 6, the decrease in -current through anode 4 caused by the X signal will actually -be less than the increase in the current through anode 84. As a consequence, the total current through resistor 15, i.e., the sum of the currents through anodes 4, 84, and 130, will increase, causing a negative signal to be applied `to grid 182. Therefore, a positive output will be obtained from the cathode of tube T7. The magnitude of the output will be proportional to the magnitude of the product of the magnitudes of the input X and Y signals. The positive polarity of the output is correct in view of both input signals.

4. Negative X and.' Y signals If the two input signals have the same magnitude as (3) above but are both negative, the output from the cathode of tube T7 will have the same magnitude and polarity.

5. Positive X and negative Y signals Assuming that the input signals have the same magnitude as in the foregoing examples but that the X signal is positive while the Y signal is negative, the total amount of current through plate resistor 15 will decrease. Therefore, the input to the grid of tube T6 will swing positive, thereby yielding a negative output from tube T7. The negative polarity of the output is correct in view of the unlike polarities of the input signals.

6. Negative X and positive Y signals Assuming that the X and Y signals have opposite polarities but the same magnitudes as the signals in (5) above, the resulting current through plate resistors 15 will be the same. Accordingly, the output from the cathode of tube T7 will have the same negative polarity and the same magnitude as the output obtained in (5) above.

Although the accelerating electrode 10 of tube T1 draws current, the amount is negligible. Moreover, even if this current were substantial, it still may be disregarded for the reason that it is a substantially constant current within the limits within which the system is operated and is divided equally between the two circuits of anodes 2 and 4.

It is to be observed that some of the Y signal applied as an input to terminal 162 is also applied to the deflecting electrode 13 via the resistors 166 and 168. The need for this is an inherent imperfection in the tube which manifests itself in a shift in current from anode 2 to anode 4 or vice versa in response to a change in beam Vdensity in the absence of a change in deflection voltage.

This imbalance is corrected by applying some of the Y signal to the deectiug plates. This imbalance correction may be applied to -deiiecting electrode 12 or to deflecting eiectrode 13, depending upon the direction of the error.

The high frequency oscillator d is used to compensate for any substantial non-uniformity in the beam pattern. Such a non-uniformity in beam pattern may be due to various things, as, for example, a defect in the cathode coating or non-uniformity of the electron optical system of the tube. If the beam pattern is not uniform, the anodes 2 and 4 will not have the same currents per unit area, and as a result, deflection of the beam may not produce equal magnitude changes in the currents of the two anodes. However, this difficulty can be overcome by oscillating the b-eam laterally at a Very high frequency which is many times the frequency of the X and Y signals. Oscillation of the beam first toward anode 2 and then toward anode 4 causes both anodes to effectively see a uniform beam. The amplitude of the lateral oscillations of the beam is small compared to the normal multiplier excursions of the beam in response to changes in X. Since the normal type of beam tube T1 utilizable in the present invention is capable of switching from one anode to the other at frequencies as high as 100 megacycles, it is preferred that the oscillator 56 have an output frequency in the megacycle range. However, oscillator 56 may be designed to modulate the beam at much lower frequencies, including frequencies in the audio range. All that is necessary is that the modulating frequency be substantially larger than the maximum frequencies of the X and Y signals so as to prevent it from introducing an erroneous variation in the output. By keeping the modulating frequency at a higher value, it is an easy matter to filter it from the output.

Of course, the oscillator 56 and the transformer 34 should be designed to have negligible effect on the circuit parameters of tube T1. Otherwise the advantage of laterally oscillating the beam will be more than offset by the error resulting from disturbance of the tubes operating parameters.

Obvious'ty, many modifications and variations of the present invention are possible in the light of the above teachings. It is to be understood, therefore, that the invention is not limited in its application to the details of construction and arrangement of parts specifically described or illustrated, and that within the scope of the appended claims it may be practiced otherwise than a specifically described or illustrated.

I claim:

1. Apparatus for multiplying together two analog voltages, said apparatus comprising (l) a tube having a cathode adapted to emit a beam of electrons, first and second anodes positioned to receive said beam, and a pair of defiecting plates for deflecting said beam from one to the other of said anodes in accordance with the voltage difference between said defiecting plates, (2) means for establishing a first current, (3) means for aut-omatically varying the intensity of said first current in accordance with a first analog signal voltage, (4) means for establishing a second current, (5) means for automatically varying the intensity of said second current in accordance with a second analog signal voltage, (6) means for establishing a Voltage difference between said plates, (7) means for varying the voltage difference 4between said deflecting plates in accordance with one of said analog signal voltage, (8) means for varying the intensity of said beam in accordance with the other of said analog signal voltages, and (9) means for producing an 'output voltage proportional to the product of said first and second analog voltages in response to the sum of said rst and second currents and the beam current through one of said anodes.

2. Apparatus as defined by claim 1 wherein said second current and the beam current through said one anode are generated by a single constant current generator.

3. Apparatus as defined by claim 1 further including means for maintaining constant the sum of said first and second currents and the beam current through said one anode when one of said analog voltages is zero.

4. A multiplier comprising a first source of constant current, means providing first and second parallel paths for a portion of said current, means providing third and fourth parallel paths for another portion of said saine current, means for oppositely varying the magnitudes of said portions automatically in response to a first analog voltage, a second source of constant current, means providing fifth and sixth parallel paths for said second constant current, means for oppositely varying the currents in said fifth and sixth paths automatically in response to a second analog signal voltage, means for oppositely Varying the currents in said first and second paths automatically in response to said second analog signal voltage, and means for producing an output signal voltage proportional to the product of said first and second voltages in response to variations in the sum of the currents in said first, third, and fifth paths.

5. A multiplier as defined by claim 4 wherein said first path is `between the cathode `and a first anode of a multielement tube and said second path is between said same cathode and a second anode within said tube.

6. A multiplied as defined by claim 5 wherein said means for oppositely varying the currents in said first and second paths in response to said second analog signal Voltage comprises a pair of deflecting electrodes for deflecting cathode-emitted electrons toward one or the other of said first and second anodes.

7. A multiplier as defined by claim 4 further including means for balancing the currents in said first and second parallel paths in the absence of said second analog signal voltage.

8. A multiplier as defined by claim 4 further including means for balancing the currents in said third and fourth paths.

9. A multiplier as defined by claim 4 further including means for balancing the currents in said fifth and sixth paths in the absence of said second analog signal voltage.

10. A multiplier as defined by claim 4 further including means for oppositely varying the currents in said first and second paths in synchronism with changes in the magnitudes of the portion of said first constant current passing through said third and fourth paths.

11. In a circuit for multiplying together to analog voltages, the combination comprising: (l) a tube having a cathode adapted to emit a beam of electrons, first and second anodes positioned to receive said beam of electrons, and a pair of deflecting plates for deflecting said beam from one to the other of said anodes in accordance with the voltage difference between said defiection plates, (2) first means for automatically varying the voltage difference between said defiecting plates in accordance with a first analog voltage, (3) second means for automatically varying the intensity of said beam in accordance with a second analog Volt-age, (4) means responsive both to said first and second analog voltages and to the beam current through one of said anodes for producing an output voltage proportional to the product of said first and said second voltages, and .(5) means for continuously oscillating said beam of electrons in a direction parallel to the axis of alignment of said first and said second anodes at a frequency higher than the maximum frequency of said first and said second analog signals.

12. Apparatus in accordance with claim 11 wherein the maximum displacement of said electron beam in said continuous oscillation is small compared to variations in position of said beam effected by variations in the voltage difference between said deliecting plates in response to variations in said first analog signal.

13. Apparatus in accordance with claim 11 wherein said means for continuously oscillating said electron beam comprises a high frequency oscillator coupled to one of said pair of detlecting plates.

14. Apparatus for multiplying together two analog voltages, said apparatus comprising: (1) a tube having a cathode adapted to emit a beam of electrons, lirst and second anodes positioned -to receive said beam, and a pair of deflecting plates for deflecting said beam from one to the other of said anodes in accordance with the voltage difference between said deecting plates, (2) means for establishing a rst current and for varying the intensity of said lirst current in accordance with a rst analog signal voltage, (3) means `for establishing a second current and for varying the intensity of said second current in accordance with a second analog signal voltage, (4) means for establishing a voltage difference between said delecting plates, (5) means for varying the Voltage difference between said deecting plates in accordance with said rst analog signal voltage, (6) means for varying the intensity of said beam of electrons in accordance with said -second analog signal voltage, (7) means for applying a portion of said second analog signal voltage to vary the voltage diierence between said deecting plates in accordance with variations in said second analog signal voltage, and (8) means for producing an output voltage proportional to the product of said first and second analog voltages in response to the sum of said rst and second currents and the beam current through one of said anodes.

15. Multiplying apparatus for providing the product of rst and second analog signals, comprising:

(1) a tube having means for forming an electron beam,

a pair of anodes, and Abeam deiecting electrodes for l0 varying the distribution of electron beam current between the anodes;

(2) a current impeder connected to one of the pair of anodes of the tube;

(3) means for applying the Iirst analog signal to the beam deliecting electrodes;

(4) means for varying the density of the tubes electron beam in accordance with the second analog signal;

(5) means responsive to the lirst analog signal for providing a first control current to the current impeder which maintains unchanged the total current through the impeder when the second analog signal is zero;

(6) means responsive to the second analog signal for providing a second control current to the current impeder which maintains unchanged the total current through ythe impeder when the first analog signal is zero;

(7) and means connected to the current impeder for providing an output signal.

References Cited by the Examiner UNITED STATES PATENTS 2,269,688 1/1942 Rath 332-58 2,653,184 9/ 1953 Robinson 328-231 X 2,793,320 5/ 1957 Patterson et al. 315--24 2,905,384 9/1959 Green 23S-194 3,011,026 11/1961 Druz 332-58 MALCOLM A. MORRISON, Primary Examiner. WALTER W. BURNS, JR., Examiner. 

4. A MULTIPLIER COMPRISING A FIRST SOURCE OF CONSTANT CURRENT, MEANS PROVIDING FIRST AND SECOND PARALLEL PATHS FOR A PORTION OF SAID CURRENT, MEANS PROVIDING THIRD AND FOURTH PARALLEL PATHS FOR ANOTHER PORTION OF SAID SAME CURRENT, MEANS FOR OPPOSITELY VARYING THE MAGNITUDES OF SAID PORTIONS AUTOMATICALLY IN RESPONSE TO A FIRST ANALOG VOLTAGE, A SECOND SOURCE OF CONSTANT CURRENT, MEANS PROVIDING FIFTH AN SIXTH PARALLEL PATHS FOR SAID SECOND CONSTANT CURRENT, MEANS FOR OPPOSITELY VARYING THE CURRENTS IN SAID FIFTH AND SIXTH PATHS AUTOMATICALLY IN RESPONSE TO A SECOND ANALOG SIGNAL VOLTAGE, MEANS FOR OPPOSITELY VARYING THE CURRENTS IN SAID FIRST AND SECOND PATHS AUTOMATICALLY IN RESPONSE TO SAID SECOND ANALOG SIGNAL VOLTAGE, AND MEANS FOR PRODUCING AN OUTPUT SIGNAL VOLTAGE PROPORTIONAL TO THE PRODUCT OF SAID FIRST ASND SECOND VOLTAGES IN RESPONSE TO VARIATIONS IN THE SUM OF THE CURRENTS IN SAID FIRST, THIRD, AND FIFTH PATHS. 